Journal of Sensors

Volume 2016 (2016), Article ID 7580483, 8 pages

http://dx.doi.org/10.1155/2016/7580483

## Using Quartz Crystal Microbalance for Field Measurement of Liquid Viscosities

School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 25 November 2015; Revised 20 January 2016; Accepted 20 January 2016

Academic Editor: Vincenzo Spagnolo

Copyright © 2016 Qingsong Bai and Xianhe Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The field measurement of liquid viscosities, especially the high viscous liquids, is challenging and often requires expensive equipment, long processing time, and lots of reagent. We use quartz crystal microbalances (QCMs) operating in solution which are also sensitive to the viscosity and density of the contacting solution. QCMs are typically investigated for sensor applications in which one surface of QCM completely immersed in Newtonian liquid, but the viscous damping in liquids would cause not only large frequency shifts but also large losses in the quality factor leading to instability and even cessation of oscillation. A novel mass-sensitivity-based method for field measurement of liquid viscosities using a QCM is demonstrated in this paper and a model describing the influence of the liquid properties on the oscillation frequency is established as well. Two groups of verified experiments were performed and the experimental results show that the presented method is effective and possesses potential applications.

#### 1. Introduction

The measurement of liquid viscosities is one of the most important steps in a variety of research and industrial fields. There are many techniques including capillary [1], falling body [2], oscillating [3], and ultrasonic [4] methods that can measure the viscosity of liquids. However, these commercial devices are usually costly, time consuming, and limited in the measurement range.

During the last few decades, quartz crystal microbalances (QCMs) are increasingly being studied as a sensitive, rapid, high-performance, and inexpensive microsensors capable of performing in liquid environments [5–12]. A QCM is a shear mode device consisting of a thin quartz disk sandwiched between two circular, metallic electrodes of the same diameters. The electrodes are used to excite the resonator whose frequency is inversely proportional to the thickness of the quartz plate. As a highly sensitive mass sensor, QCMs have been used in various areas of science and technology, such as mass detectors in vapors or solutions [13–16], biosensors [17, 18], and electrochemical microbalances or nanobalances [19–21].

The linear relationship between the mass change and the resonance frequency shift of the QCM is described by the Sauerbrey equation [22]:where and are mass change and frequency shift, respectively; is the operating frequency of the QCM; is the active area of the QCM electrodes; and and are the density and shear modulus of the piezoelectric quartz crystal, respectively.

It should be noted here that the Sauerbrey equation is established on the assumption that the mass change attached on the QCM surface is a rigid and even thin film. So the linear relation between the adsorbed mass and the change in frequency is not necessarily valid for viscoelastic films. Therefore, the Sauerbrey equation is invalid for the measurement of liquid parameters.

Kanazawa and Gordon II offered an additional method to measure Newtonian liquid using a QCM, namely, the total immersion of one surface of the QCM in sample liquid, and determined the behavior of the crystal/fluid system by examining the coupling of the elastic shear waves in the crystal to the viscous shear weaves in the sample liquid. In this manner, the resonance condition derives directly from the matching of appropriate boundary conditions on the shear waves. Thus, the Kanazawa model that reveals the relative relationship between the frequency shift of the QCM and the density and viscosity of the sample liquid has been developed [23]:where is the operating frequency of the QCM; and are the density and viscosity of the sample liquid, respectively; and are the density and shear modulus of the quartz having the values = 2.648 × 10^{3} kg/m^{3} and = 2.947 × 10^{11} g/cm·s^{2}, respectively.

However, there are still some inevitable drawbacks when using Kanazawa model for on-field measurement of liquid properties; that is, this method is difficult to be applied and spread widely in on-field testing because it is sample wasteful, requires complex instruments, and is difficult to operate. In addition, immersing the QCM in liquid will damp the amplitude, and the damping becomes seriously detrimental when immersed in highly viscous liquid, which will make the measurements hard or even causes the failure of oscillation.

This new mass-sensitivity-based approach presented in this paper could promote the application of QCMs in on-field testing of liquid viscosities and enable the measurement of highly viscous liquids. Thanks to the advantages of this new approach including simplicity of operation, saving reagent and time, real-time output, and label-free analysis, this novel approach will achieve a considerable potential application prospect in on-field measurements of liquids.

#### 2. Proposed Method

The frequency shift caused by a localized or nonuniform mass attached on the QCM electrodes is given by [24]where is the mass-sensitivity function, in hertz per kilogram; is the effective added mass; is the radius for the mass deposit on the electrode; and are the polar coordinates of the point at which the mass is added.

The research of Josse et al. shows that the mass-sensitivity distribution of QCM devices can be represented by the following equation [25]:where is the Sauerbrey sensitivity constant, with a value of 1.78 × 10^{11} Hz·cm^{2}/kg; is the particle displacement amplitude function; and is the distance from the center.

The particle displacement amplitude function is solution of the following particle displacement amplitude equation [26]:where represents the wavenumber; is a constant determined by the elastic stiffness constants and the piezoelectric constants of crystal quartz. Since the particle displacement and shear strain field are continuous at (where is the radius of electrode), according to these boundary conditions, the boundary equations of QCM with “m-m” type electrode are obtained as [27]

On the basis of these boundary conditions, can be determined. And the mass-sensitivity function of QCM with “m-m” type electrode is then determined [28].

Take two QCMs used in this study (AT-cut 10 MHz fundamental QCM and AT-cut 10 MHz 3rd overtone QCM), for example. The diameters of crystal and gold-electrode are 8.7 mm and 4 mm, respectively. The thickness of the gold-electrode is 1000 Å. The profile of mass-sensitivity distribution can be obtained as shown in Figures 1 and 2, respectively.